Book•
Computational Aspects of Vlsi
01 Jan 1984-
About: The article was published on 1984-01-01 and is currently open access. It has received 862 citations till now. The article focuses on the topics: Very-large-scale integration.
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01 Jan 1998
TL;DR: This paper presents two optimal algorithms to compute the contour of maximal elements of a set of planar points on an k-constrained RM of size p, p p, k p, and the second algorithm solves this problem of size n in O( q k ) time.
Abstract: The Recon gurable Mesh (RM) attracted criticism for its key assumption that a message can be broadcast in constant time independent of bus length. To account for this limit Beresford-Smith et al. have recently proposed k-constrained RM where buses of length at most k, a constant, are allowed to be formed. Straightforward simulations of optimal RM algorithms on this constrained RM model are found to be non-optimal. This paper presents two optimal algorithms to compute the contour of maximal elements of a set of planar points. The rst algorithm solves this problem of size p in O( p k ) time on an k-constrained RM of size k p, k p, and the second algorithm solves this problem of size n in O( q k ) time on an k-constrained RM of size p q, p q, and pq = kn.
1 citations
Cites methods from "Computational Aspects of Vlsi"
...Other than the buses and switches the RM of size p q is similar to the standard mesh of size p q and hence it has (pq) area in VLSI embedding [17], under the assumption that processors, switches, and links between adjacent switches occupy unit area....
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21 Mar 1990
TL;DR: An efficient algorithm for broadcasting in a cube-connected-cycles network containing faulty nodes/links is proposed, which is particularly useful in critical real-time systems that cannot tolerate the time overhead of identifying the faulty processors online.
Abstract: An efficient algorithm for broadcasting in a cube-connected-cycles network containing faulty nodes/links is proposed. The algorithm is particularly useful in critical real-time systems that cannot tolerate the time overhead of identifying the faulty processors online. The algorithm delivers multiple copies of the broadcast message through disjoint paths to all the nodes in the system. The salient feature of the proposed algorithm is that the delivery of the multiple copies is transparent to the processors receiving the message and does not require the processes to know the identity of the faulty processors. The processes on nonfaulty nodes that receive the message identify the original message from the multiple copies using some scheme appropriate for the fault model used. The number of steps in which the algorithm completes if it can use all or at most one of its outgoing nodes is determined. >
1 citations
Posted Content•
TL;DR: It is shown that for every 3-connected planar graph, there exists a simultaneous representation of the graph and its dual with 3D boxes, and a linear-time algorithm is given for constructing such a representation.
Abstract: We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there exists a simultaneous representation of the graph and its dual with 3D boxes. We give a linear-time algorithm for constructing such a representation. This result extends the existing primal-dual contact representations of planar graphs in 2D using circles and triangles. While contact graphs in 2D directly correspond to planar graphs, we next study representations of non-planar graphs in 3D. In particular we consider representations of optimal 1-planar graphs. A graph is 1-planar if there exists a drawing in the plane where each edge is crossed at most once, and an optimal n-vertex 1-planar graph has the maximum (4n - 8) number of edges. We describe a linear-time algorithm for representing optimal 1-planar graphs without separating 4-cycles with 3D boxes. However, not every optimal 1-planar graph admits a representation with boxes. Hence, we consider contact representations with the next simplest axis-aligned 3D object, L-shaped polyhedra. We provide a quadratic-time algorithm for representing optimal 1-planar graph with L-shaped polyhedra.
1 citations
Cites background from "Computational Aspects of Vlsi"
...Contact representations of graphs have practical applications in data visualization [42], cartography [37], geography [45], sociology [29], very-large-scale integration circuit design [46], and floor-planning [34]....
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Dissertation•
01 Dec 1985
TL;DR: A graph-theoretic compaction algorithm is developed for the compaction of symbolically specified layouts of building block LSI's, which outlines a method for modifying the constraint-graph, in place, such that the modified graph represents the jogged layout.
1 citations
TL;DR: This paper is a brief survey of the highlights of the studies of uniformities in algebraically specified graphs, and is both fitting and pleasureful to dedicate this survey to Bob McNaughton, a wise mentor and a man of vision.
Abstract: This survey acknowledges an intellectual debt to Bob McNaughton. In 1968 I turned my research focus to the study of structural uniformities in graphs, motivated by the desire to study theoretical aspects of data structures. The approach that I took in this study was influenced heavily by the algebra-based study of structure in finite automata initiated in the mid-1960s by Bob and others. Their successes in using the syntactic monoid of an automaton to study its structure convinced me to base my study on a monoid-theoretic specification of graphs. The study of what I termeddata graphs occupied me for the next 4–5 years; the insights garnered during that period have served me well since, in a variety of disparate contexts. Indeed, when I began to focus on the study of structural uniformities in the interconnection networks of parallel architectures, in the mid-1980s, it was second nature to me to base this study also on a monoid-theoretic specification of the graphs underlying the interconnection networks. This paper is a brief survey of the highlights of my studies of uniformities in algebraically specified graphs. It is both fitting and pleasureful to dedicate this survey to Bob McNaughton, a wise mentor and a man of vision.
1 citations